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>> Converting impedances from

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a delta connection to

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a Y connection or from a Y[br]connection to a delta connection,

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is analogous to what we saw when we[br]were dealing strictly with resistances.

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Again, what we mean when[br]we say that one say that

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Y circuit is consistent or is[br]equivalent to a delta connection.

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By that, we mean that the impedance

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seen looking in between[br]any two terminals is the same,

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whether it is connected in Y or

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connected in delta and when you

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compare these with those that we saw[br]with working with straight resistances,

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you'll see that[br]the same relationships hold.

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On this side here we have the Y to

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delta connection and[br]here we have converting

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delta connected load to a Y connected load.

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So, the Y connected load impedances[br]are Z_1, Z_2 and Z_3.

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The delta connected as Z_a, as Z_b and Z_c,

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where Z_1 is connected to node one,

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Z_2 is connected to node two,

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Z_3 is connected to node three and Z_a

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is the impedance opposite[br]the number one terminal,

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Z_b is the impedance opposite[br]the number two terminal

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and Z_c is the impedance[br]opposite the third terminal.

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Now, these become interesting,

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even more interesting than they[br]already are and the circumstances when

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Z_1 equals Z_2 equals Z_3 or you[br]got a balanced three-phase load.

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Under those circumstances, when Z_1

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equals Z_2 equals Z_3, we'll call that Z_y.

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When that is the case,

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then Z_a equals Z_b equals Z_c.

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We'll call that Z Delta is equal to.

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If this Z is the same, you have one, two,

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three, Z_y squared divided by Z_y.

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So, Z Delta then is equal[br]to three times Z_y,

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and over here you do[br]a similar situation where

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Z_a equals Z_b equals Z_c equals,

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call that again Z delta,

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then Z_1 equals Z_2 equals Z_3,

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call that Z_y and that is then here

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you'd have Z Delta squared[br]over three Z delta,

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or Z_y then is equal to[br]Z Delta divided by three.